相关论文: Commutators of flows and fields

Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…

This work introduces the framed curvature flow, a generalization of both the curve shortening flow and the vortex filament equation. Here, the magnitude of the velocity vector is still determined by the curvature, but its direction is given…

Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…

A classical result in Differential Geometry states that the flows of two smooth vector fields commute if and only if their Lie Bracket vanishes. In this work, we extend this result to a more general setting where one of the vector fields is…

Extending It\^o's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It\^o, applies to one dimensional semimartingales and convex functions.…

We prove an implicit function theorem for non-commutative functions. We use this to show that if $p(X,Y)$ is a generic non-commuting polynomial in two variables, and $X$ is a generic matrix, then all solutions $Y$ of $p(X,Y)=0$ will commute…

The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…

We establish the existence of one-parameter families of helicoidal surfaces of $\mathbb H^2\times\mathbb R$ which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.

In part I of this paper, I proposed a new set of equations, which I refer to as the M(D,{\eta})-formulation and which differs from the Navier-Stokes-Fourier description of fluid motion. Here, I use these equations to model several classic…

The quotients $Y=X/conj$ by the complex conjugation $conj\: X\to X$ for complex rational and Enriques surfaces $X$ defined over $\R$ are shown to be diffeomorphic to connected sums of $\barCP2$, whenever $Y$ are simply connected.

A soliton of the mean curvature flow in the product space $\mathbb{s}^2\times\mathbb{R}$ as a surface whose mean curvature $H$ satisfies the equation $H=\langle N,X\rangle$, where $N$ is the unit normal of the surface and $X$ is a Killing…

In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The…

In this note, we introduce a new curvature condition called the $2-$positive bisectional curvature on compact K\"{a}hler manifolds. We then deduce a characterization theorem for manifolds with $2-$positive bisectional curvature, which can…

Under general conditions, the equation $g(x,y) = 0$ implicitly defines $y$ locally as a function of $x$. In this article, we express divided differences of $y$ in terms of bivariate divided differences of $g$, generalizing a recent result…

We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savar\'e, to CAT(1)-spaces. The key tool is the so-called "commutativity" representing a Riemannian nature of the…

We study the behavior of the Yang-Mills flow for unitary connections on compact and non-compact oriented surfaces with varying metrics. The flow can be used to define a one dimensional foliation on the space of SU(2) representations of a…

We prove that a function $f(x,y)$ of real variables defined on a rectangle, having square integrable partial derivatives $f"_{xx}$ and $f"_{yy}$, has almost everywhere mixed derivatives $f"_{xy}$ and $f"_{yx}$.

In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…

We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.